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## Homework Statement

A cylindrical shaped tin can must have a volume of 1000cm

^{3}.

Find the dimensions that require the minimum amount of tin for the can (Assume no waste material). The smallest can has a diameter of 6cm and a height of 4 cm.

## Homework Equations

[tex]V = \pi r^{2}h[/tex]

[tex]P = 2( \pi r^{2}) + (2 \pi r)h[/tex]

## The Attempt at a Solution

I basically start off by isolating a variable:

[tex]V = \pi r^{2}h[/tex]

[tex]1000 = \pi r^{2}h[/tex]

[tex]318.3 = r^{2}h[/tex]

[tex]r^{2} = \frac{318.3}{h}[/tex]

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This is where I'm stuck. Do I plug this into the surface area formula.

I know I have to sub this into something else, and then expand and find the derivative of that new equation to find where h > 4.

Just need to find out what to do next from here.

Thanks for any help!